Nonlinear analysis of a rotating pre-twisted composite blade reinforced with functionally graded graphene platelets under axial and transverse excitations

Due to the harsh service environment and multiple loads, studying the nonlinear vibration characteristics of rotating blades under complex loads is necessary. The new axial force model assumed as a combined force including the non-uniform aerodynamic force in the tip clearance and blade-casing local rubbing force is proposed for the first time in this paper. The nonlinear analysis of a rotating pre-twisted composite blade reinforced with functionally graded graphene platelet (FGGP) is investigated under axial and transverse excitations. The blade is treated as FGGP-reinforced rotating twisted cantilever plate. The transverse excitation caused by subsonic airflow is derived by using the vortex lattice method. The blade-casing local rubbing and non-uniform axial force dynamic change when the blade is rotating. Based on von-Karman nonlinear geometric assumptions and Lagrange equation, the governing equations of motion for the FGGP-reinforced rotating twisted plate are derived. The averaged equations under the case of primary resonance and 1:2 internal resonance are obtained by the multiple scale method. Comparisons of frequencies and modes in the present method are carried out. The results are in good agreement with other literature. The amplitude-frequency and amplitude-force curves, bifurcations, and chaotic motions of the FGGP-reinforced rotating twisted cantilever plate under axial and transverse excitations are discussed. The results show that the nonlinear vibrations are complex when 1:2 internal resonance and primary resonance of the FGGP-reinforced rotating twisted composite blade occur. The amplitude of the blade is higher with the bigger axial force. At the same time, with the increase of axial force and incoming flow speed, the motion of the blade changes from periodic to chaotic. The interesting phenomena of inverse period-doubling bifurcations are found.